# Why do we write wave function for electronic transition in molecules like this?

Why do we write transition between two different electronic states like that: $$\bar p_{if}=\langle \psi_i|\bar p|\psi_f \rangle$$ And not like that: $$\bar p_{if}=\langle \psi_f|\bar p|\psi_i \rangle$$ where $$i$$ and $$f$$ mean initial and final states. As I understand, we want to see how much those states overlap each other, but why are we using operator on final state?

The two numbers are complex conjugate of each other - thus, whatever is the calculation, they are manipulated to give something real. E.g., in the at lowest order we simply use the Fermi Golden rule $$w_{i\rightarrow f} \propto |\langle \psi_i|\bar{p}|\psi_f\rangle|^2= \langle \psi_i|\bar{p}|\psi_f\rangle\langle \psi_i|\bar{p}|\psi_f\rangle^*= \langle \psi_i|\bar{p}|\psi_f\rangle\langle \psi_f|\bar{p}|\psi_i\rangle.$$